What is the most important point of Huygens' wave theory?

Assertion $A$: For light diverging from a point source,the intensity at the wavefront does not depend on the distance.
Reason $R$: In a diverging beam of light from a point source,a spherical wavefront is observed.

Explain the refraction of a plane wave from a denser to a rarer medium using Huygens' principle.

If $AB$ is an incident plane wave front,then what will be the refracted wave front for a lens with refractive index $n_2 > n_1$?

$A$ light wave travels in a vacuum along the $x$-axis. Which of the following may represent the wave front?

Initially,parallel cylindrical wavefronts travel in a medium with a refractive index $\mu(I) = \mu_0 + \mu_2 I$,where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity. The intensity decreases as the radius increases. What happens when it enters the second medium?